QuestionJune 19, 2025

A metal rod of mass m carrying a current I glides on two horizontal 'rails a distance d apart. If the coefficient of kinetic friction between the rod and rails is mu _(k') what vertical magnetic field is required to keep the rod moving at a constant speed? (Use any variable or symbol stated above along with the following as necessary: g.) B=(mu _(k)mg)/(Id)

A metal rod of mass m carrying a current I glides on two horizontal 'rails a distance d apart. If the coefficient of kinetic friction between the rod and rails is mu _(k') what vertical magnetic field is required to keep the rod moving at a constant speed? (Use any variable or symbol stated above along with the following as necessary: g.) B=(mu _(k)mg)/(Id)
A metal rod of mass m carrying a current I glides on two horizontal 'rails a distance d apart. If the coefficient of kinetic friction between the rod and rails is mu _(k') what vertical magnetic field is required to keep the rod moving at a constant speed? (Use any variable or symbol stated above along with the following as necessary: g.) B=(mu _(k)mg)/(Id)

Solution
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Answer

B = \frac{\mu_k \cdot m \cdot g}{I \cdot d} Explanation 1. Identify Forces The rod experiences a magnetic force F_B = I \cdot d \cdot B and a frictional force F_f = \mu_k \cdot m \cdot g. 2. Set Forces Equal for Constant Speed For constant speed, set F_B = F_f. Thus, I \cdot d \cdot B = \mu_k \cdot m \cdot g. 3. Solve for Magnetic Field B Rearrange to find B: B = \frac{\mu_k \cdot m \cdot g}{I \cdot d}.

Explanation

1. Identify Forces<br /> The rod experiences a magnetic force $F_B = I \cdot d \cdot B$ and a frictional force $F_f = \mu_k \cdot m \cdot g$.<br /><br />2. Set Forces Equal for Constant Speed<br /> For constant speed, set $F_B = F_f$. Thus, $I \cdot d \cdot B = \mu_k \cdot m \cdot g$.<br /><br />3. Solve for Magnetic Field $B$<br /> Rearrange to find $B$: $B = \frac{\mu_k \cdot m \cdot g}{I \cdot d}$.
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